Think at the margin: one more unit, its extra cost and extra benefit

Grade 12 Social Studies Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Cards A and B on study time (all made up for practice). Card A, "Rosa's study time (made up)". Written for this sheet. Table, columns Hour of study | Extra test points it adds: 1st | 12; 2nd | 8; 3rd | 5; 4th | 2. Card B, "What an hour costs (made up)". Written for this sheet. Summary in our words, not a quotation: each hour Rosa studies means one less hour of babysitting at $6 an hour. Rosa values each test point at $1. Later the babysitting pay falls to $4 an hour.

2. 1.

   Ari reads cards A and B. How many hours should Rosa study at $6 an hour?

   • One: the 1st hour adds the most points, $12, so Rosa should stop after the best hour
   • Two: the 2nd hour adds $8 of value, above its $6 cost, but the 3rd adds only $5
   • Three: the 3 hours add 25 points in total, which is more than the $18 they cost
   • Four: every hour adds some points, so Rosa should keep studying until the points stop
3. 2.

   Babysitting pay falls to $4 an hour. Esme uses card A. How does Rosa's best number of study hours change?

   • It rises to three: the 3rd hour adds $5, above its new $4 cost, but the 4th adds only $2
   • It falls to one, since a babysitting pay of $4 means studying is a smaller gain than before
   • It rises to four, since a $4 cost makes each hour worth taking until the points run out
   • It stays at two, since the number of hours depends on the points each hour adds and not on its $4 cost
4. 3.

   A friend says four hours bring 27 points, or 6.75 a point per hour, well above $6, so Rosa should study four hours. Jun tests this. What is the verdict?

   • Wrong: the average hour adds $6.75, but the 4th hour adds only $2, below its $6 cost
   • Right: the 4th hour adds $2, and any gain at all is worth having when studying is the goal
   • Wrong: 6.75 is not a whole number, so the friend's average cannot be used for hours of study
   • Right: four hours add $27 in all, an average of $6.75 an hour, which beats the $6 cost of an hour

5. Use this

   Cards A and B on two bakers (all made up for practice). Card A, "Two bakers (made up)". Written for this sheet. Table, columns | Loaves in a day | Cakes in a day (each baker does one or the other, or splits the day): Rosa | 12 | 6; Tim | 4 | 4. Card B, "Rosa's idea (made up)". Written for this sheet. Summary in our words, not a quotation: Rosa bakes more of both than Tim, so she says she should bake everything and leave Tim out.

6. 4.

   Tim bakes only cakes and Rosa only loaves, and they trade 3 loaves for 2 cakes. Zee checks the trade. Does each baker gain?

   • Neither gains, since they swap 3 loaves for 2 cakes and what one gets the other gives up
   • Yes: Rosa pays 1.5 loaves a cake instead of 2, and Tim gets 1.5 loaves a cake instead of 1
   • Tim alone gains, since he bakes the cakes and receives loaves that Rosa found easy to make
   • Rosa alone gains, since she is better at both jobs and receives the cakes she wanted
7. 5.

   Kira tests Rosa's idea on card B with card A. What is the verdict?

   • Weak: trading loaves for cakes costs Rosa 1.5 loaves a cake instead of 2, so she ends with more
   • Weak: Rosa should bake nothing and let Tim do the baking, since Tim's cakes are cheaper
   • Strong: Rosa makes more of both goods per day, so she would produce more by working alone
   • Strong: Tim bakes less of both, so leaving Tim out costs Rosa nothing she would miss

8. Use this

   Cards A and B on income tax (card A is IRS data; card B is made up). Card A, "Federal income tax brackets for 2024, single filers". Source: Internal Revenue Service, IRS provides tax inflation adjustments for tax year 2024 (irs.gov), read Nov 14, 2026. Summary in our words, not a quotation: the rate is 10 percent on taxable income up to $11,600; 12 percent on the part over $11,600 up to $47,150; 22 percent on the part over $47,150 up to $100,525; and 24 percent on the part over $100,525 up to $191,950. Each rate applies only to the part of income inside its bracket. Card B, "Noor's year (made up)". Written for this sheet. Summary in our words, not a quotation: Noor is single and has $50,000 of taxable income in 2024. Noor is offered a $1,000 bonus for a weekend of extra work.

9. 6.

   Milo reads cards A and B. How much of the $1,000 bonus does Noor keep, and why?

   • $780: the bonus falls in the 22 percent bracket, so $220 goes to tax
   • $760: the bonus is taxed at 24 percent, the next bracket, because it is a large extra payment
   • About −$4,000: the bonus lifts Noor's whole pay into the 22 percent bracket, so tax jumps
   • $880: the bonus is taxed at the 12 percent rate that most of Noor's income pays
10. 7.

    Bo reads cards A and B. What are Noor's average tax rate and marginal tax rate on $50,000?

    • The average rate is about 12 percent ($6,053 on $50,000); the marginal rate, on the next dollar, is 22 percent
    • Both rates are 12 percent, since most of Noor's $50,000 lies in the 12 percent bracket
    • The average rate is 22 percent and the marginal rate is about 12 percent, the rate on most of Noor's $50,000
    • Both rates are 22 percent, since Noor's $50,000 reaches the 22 percent bracket and that rate applies throughout
11. 8.

    Noor values the free weekend at $850. Luz uses cards A and B. Should Noor take the bonus work?

    • Yes: the bonus is $1,000, which is more than the $850 Noor puts on the free weekend
    • No: after tax the weekend pays $780, less than the $850 Noor puts on the free time
    • No: tax takes over half of a bonus, so extra work does not pay for Noor
    • Yes: the bonus is taxed at the 12 percent rate, so Noor keeps $880, more than $850

12. Use this

    Card A on a ticket and a shift (all made up for practice). Card A, "Lena's evening (made up)". Written for this sheet. Summary in our words, not a quotation: Lena paid $40 for a concert ticket that cannot be refunded or sold. On the night Lena has a cold, and the concert is now worth $20 to Lena. A cafe offers Lena a shift at the same time, paying $60. The shift costs Lena $25 in effort.

13. 9.

    Noah reads card A. What should Lena do, and why?

    • Go to the concert: Lena paid $40, and skipping it would waste that money
    • Work the shift because it pays $60, more than the $40 the ticket cost Lena
    • Work the shift: it nets $35, more than the concert's $20, and the $40 ticket is spent either way
    • Go to the concert: it is worth $20 to Lena tonight, and the shift is just a chore
14. 10.

    Ren lists four claims about card A. Which one goes beyond what the card shows?

    • Buying the ticket was a mistake, because Lena now loses $40 whatever Lena does
    • The shift pays $60 and costs Lena $25 in effort, a net of $35
    • The $40 for the ticket cannot be recovered, whether Lena goes to the concert or not
    • Going to the concert means giving up a shift that would net Lena $35